The Search for a More Perfect Kilogram

The official US kilogram — the physical prototype against which all weights in the United States are calibrated — cannot be touched by human hands except in rare circumstances. Sealed beneath a bell jar and locked behind three heavy doors in a laboratory 60 feet under the headquarters of the National Institute of Standards and Technology 20 miles outside Washington, DC, the shiny metal cylinder is, in many ways, better protected than the president.

“Everything is a potential contaminant,” says Patrick Abbott, a NIST physicist responsible for maintaining it. “There are hydrocarbons on people. There’s water in the air.”

The American prototype is one of some four dozen such national standards around the world, and each of those, in turn, is accountable to an even higher authority: a regal artifact called the international prototype kilogram. Familiarly known as Le Grand K and held in a vault just outside of Paris under three bell jars, it dates back to the 1880s, when it was forged by the British metallurgist George Matthey from an alloy of nine-tenths platinum and one-tenth iridium. As a metric unit, the kilogram is “equal to the mass of the international prototype,” according to the official definition. In other words, as metrologists like to point out, it has the remarkable property of never gaining or losing mass. By definition, any physical change to it alters the mass of everything in the cosmos.

Aside from a yearly ceremonial peek inside its vault, which can be unlocked only with three keys held by three different officials, the prototype goes unmolested for decades. Yet every 40 years or so, protocol requires that it be washed with alcohol, dried with a chamois cloth, given a steam bath, allowed to air dry, and then weighed against the freshly scrubbed national standards, all transported to France. It is also compared to six témoins (witnesses), nominally identical cylinders that are stored in the vault alongside the prototype. The instruments used to make these comparisons are phenomenally precise, capable of measuring differences of 0.0000001 percent, or one part in 1 billion. But comparisons since the 1940s have revealed a troublesome drift. Relative to the témoins and to the national standards, Le Grand K has been losing weight — or, by the definition of mass under the metric system, the rest of the universe has been getting fatter. The most recent comparison, in 1988, found a discrepancy as large as five-hundredths of a milligram, a bit less than the weight of a dust speck, between Le Grand K and its official underlings.

This state of affairs is intolerable to the guardians of weights and measures. “Something must be done,” says Terry Quinn, director emeritus of the International Bureau of Weights and Measures, the governing body of the metric system. Since the early 1990s, Quinn has campaigned to redefine the kilogram based not on a physical prototype but on a constant of nature, something hardwired into the circuitry of the universe. In fact, of the seven fundamental metric units — the kilogram, meter, second, ampere, kelvin, mole, and candela — only the kilogram is still dependent on a physical artifact. (The meter, for example, was redefined 30 years ago as the distance traveled by light in a given fraction of a second.)

Two different approaches to linking the kilogram to a fundamental constant are in the works, but both have proven far more complicated than in the case of the meter. Borrowing tricks from quantum mechanics and techniques used to manufacture atomic bombs, the competing initiatives are finally on the verge of delivering the kind of precision necessary to displace Le Grand K. In anticipation of that achievement, the General Conference on Weights and Measures will vote this month on a proposal to redefine the kilogram based not on a physical artifact but on a fundamental constant. Approval requires a majority of the 55 member states assembled in Paris to vote for the proposal.

The outcome of the ballot is anything but certain. Many metrologists accustomed to venerating the platinum-iridium cylinder are wary of change. “The best thing is to wait,” Abbott says. But as the technologies needed to realize the two competing definitions have matured, Quinn has gained the support of influential scientists such as physicist Barry Taylor of NIST and Nobel Prize-winning physicist Bill Phillips. If the idea of a fundamental constant wins approval, Le Grand K will be on its way to becoming nothing more than a $56,000 hunk of metal.

No one can say for sure why the prototype and its brethren are drifting apart. One rather obvious possibility, suggested by Taylor, is that the national prototypes and even the témoins have been used more often than Le Grand K, which has been handled only three times since 1889. The handling could subtly contaminate the surface. A more exotic theory posits that slight variations in Matthey’s alloy lead to different rates of outgassing, the technical term for the gradual escape of gases trapped in the metal. Whatever the explanation, the divergence is problematic, and not only for theoretical reasons. In fields ranging from particle physics to global commerce, the erratic behavior of the master kilogram shows that a system of measurement based on a physical artifact can’t be trusted. “This is simply not a satisfactory situation,” Quinn says. “You have an object made with the technology of the 19th century upon which a very large proportion of modern measurements are based — not just mass, but electrical measurements and measurements of force and heat and light.” The metric energy unit known as the joule, for example, is defined in terms of the work needed to move a 1-kilogram mass a given distance over a given time period. And the luminosity of light, or candela, is measured in terms of power, designated in watts, or joules per second. In other words, if the kilogram is unreliable, the joule and the candela become unreliable as well. Nobody at the grocery store is fretting over whether a kilo of bananas is a speck of dust lighter or heavier than in their great-grandparents’ era, but the change could eventually matter enormously to engineers optimizing computers and fiber-optic networks.

Today the kilogram is calibrated to a metal slug in Paris, but in the future we might instead rely on the exact number of atoms in a silicon sphere.Photo: Christopher Griffith; kilogram models by Jim Zivic

The practical issues alone are enough to make redefining the kilogram essential, but there’s also a weighty philosophical matter to consider. To Quinn and his supporters, the continued use of the decaying Grand K represents a betrayal of the ideals on which the metric system was founded. When first conceived in 1791, in revolutionary France, the system was intended to be “for all people, for all time,” in the famous phrasing of the French savants (as Enlightenment philosopher-scientists immodestly called themselves). Back then, their intervention was sorely needed. The reigning standard of length in Paris, the toise, was defined by an iron rod embedded in a courthouse staircase in 1668. Outside Paris, chaos ruled: There were some 250,000 local units of weights and measures in France alone, many of them sharing the same names, a fact that ensured that the only constant was confusion.

In place of these, the French Academy of Sciences proposed in 1791 to create an entirely new system that would govern all of France and eventually the world. Fittingly, the new unit of length would derive from the size of the world itself, specifically its circumference. “It was an incredibly astute political move to base measurement on the globe we all share,” says Ken Alder, a Northwestern University historian who is one of the world’s foremost experts on metric history.

First, though, the meridian circumference of Earth had to be measured with unprecedented precision. Two savants were dispatched from Paris in opposite directions, one toward Dunkirk and the other toward Barcelona. Each was tasked with mapping out a larger-than-life trigonometry problem, to measure the distance they traveled as a chain of imaginary triangles based on lines of sight between high points like mountaintops and church steeples. In the chaos of revolution and war with Spain, the surveying savants were frequently mistaken for spies and occasionally imprisoned. Originally slated to last a year, their quest stretched to seven, outlasting the reigns of Louis XVI and Robespierre and extending to the eve of Napoleon’s. The plan was to define the meter as one ten-millionth of the distance from the North Pole to the equator; the kilogram, in turn, was defined as the mass of a cubic decimeter of rainwater at 4 degrees Celsius, translated for practical reasons into a platinum cylinder, the 18th-century prototype for the 19th-century international prototype still in use today.

Two hundred years after the Barcelona-to-Dunkirk survey, Quinn considers a redefinition based on physical constants to be nothing less than historical destiny. The French academy envisioned “a system that would not be based on any particular artifact,” he says. “But it just was not possible then. If we move to a system that is based on the fundamental constants of physics, we will have achieved what the great savants of the 18th century set out to achieve but couldn’t.”

As the name suggests, constants are consistent no matter where you measure them. The gravitational attraction between a star and planet will be the same in Andromeda as in the Milky Way. The speed of light, too, is consistently the same in a vacuum: 299,792,458 meters per second. Starting in 1889, the meter was defined in terms of a physical artifact akin to the kilogram prototype: a platinum-iridium rod cast by Matthey and stored in a vault outside Paris, alongside Le Grand K. But in 1983, the relationship between the meter and the speed of light was officially inverted, with the meter being redefined as “the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.” (The second, in turn, being defined by certain fundamental properties of the cesium 133 atom.)

Why has it taken so much longer to yoke mass to the laws of nature than it did with length? The issue is precision. By the 1980s, the speed of light had been measured to nine significant digits, so the meter’s redefinition based on this constant was more precise than the best contemporary measurements of physical objects had been. For mass, by contrast, the two most promising constants — Avogadro’s, which would relate the kilogram to the mass of a single atom, and Planck’s, which would relate it to units of energy — had been measured with confidence to only six digits. (Today, this has improved to nearly eight.) In the notation of physics, both have 4.4 x 10-8uncertainty, meaning that the experiments have not nailed down a precise value for that all-important eighth digit. Before any redefinition is possible, one of these constants will need to be determined experimentally to enough decimal places that it will be as accurate and reliable as Le Grand K. “I thought it would take five years,” Quinn confesses nearly two decades into the quest.

Team Avogadro is based in Brunswick, Germany, at the Physikalisch-Technische Bundesanstalt, the German equivalent of NIST. Over lunch in the cafeteria, physicist Arnold Nicolaus extols the historic significance of the project that he and his fellow metrologists are undertaking. “It is a special thing to make a redefinition,” he says. “For hundreds of years, you will find in the history books the three or four people who changed the kilogram.” We are joined for coffee by Peter Becker, whose 30 years of research into the measurement of silicon lattices may make the redefinition possible. In the early 1970s, his team started firing x-rays at silicon crystals to see how much space there was between atoms. “But back then there was no discussion of replacing the kilogram using these experiments,” he says. “We were working only to estimate the Avogadro constant.”

The ideas underlying that constant date back to 1811, when Italian scientist Amedeo Avogadro proposed a method of comparing the atomic mass of various elements by comparing the volume of different gases at the same temperature and pressure. Using this reasoning, it’s possible to work out a fundamental unit of mass — that of a hydrogen-1 atom with its single proton and no neutrons — expressed as a natural constant. Theoretically, the kilo could then be expressed as the mass of a specific quantity of hydrogen atoms. Of course, the number would be unfathomably large: A mere gram of hydrogen contains more than 600 billion trillion atoms, or a 6 followed by 23 zeros. That’s a lot of counting.

Richard Steiner proposes defining the kilogram by how much electrical force it takes to levitate Le Grand K in a machine called a watt balance.Photo: Ian Allen

So two decades ago, as Quinn’s campaign to switch the kilo to a physical constant began to gain traction, Becker and his colleagues decided to tackle the problem from the opposite direction. Building upon their earlier work, they decided to create a 1-kilogram sphere, not from hydrogen, but from silicon. The sphere would be identical in mass to the international prototype. Then, because Becker’s x-ray experiments had shown that the atoms were arranged in a regular pattern, they could use basic geometry to deduce how many silicon atoms the crystalline sphere contained. Once the number of atoms was determined with sufficient precision, that figure would forever define the mass of the kilogram. In other words, they set out to make a new artifact superior to Le Grand K — but only so that they could count its atoms and then eliminate all kilogram artifacts in perpetuity.

To improve on the precision of his result from the 1970s and ’80s, Becker needed to reduce the irregularity of his silicon surfaces. He commissioned one of the world’s most renowned lensmakers — a German immigrant in Australia named Achim Leistner — to craft the most perfect sphere ever created, a flawless orb honed precisely to the mass of Le Grand K.

Leistner describes his job as “massaging atoms.” He works by hand because he believes — and the most advanced computer imaging has confirmed — that no machine can match his touch. Taking a 1.01-kilogram silicon ball crudely cut on a 3-D lathe to within 10 micrometers of sphericity, Leistner spends several months polishing the surface by spinning the object inside a pair of funnels — like a scoop of ice cream held between two cones — until he can feel the molecular structure of the cubic silicon crystal itself with his fingertips, 12 edges and eight corners barely protruding from the rounded surface. Then the hard work begins. Without letting the mass of the sphere drop below the 1-kilogram mass of the international prototype, Leistner must polish each of the nearly imperceptible edges and corners, removing mere nanometers of material per week. Since a several-atom layer of silicon dioxide (more familiarly known as quartz) forms on the surface whenever he stops spinning the sphere, and since quartz is much harder than pure silicon, he can spend as many as six hours a day carefully buffing off the oxide layer before reaching the silicon atoms to be shaved.

Resting on a tabletop in Nicolaus’ lab, amid a mess of latex gloves and rags, is Leistner’s best effort to date, a sphere of staggering exactitude that was crafted in the late ’90s. It appears to emit a preternatural light, like a crystal ball that might reveal Avogadro’s constant if only one stared at it just right. “If this sphere were the size of Earth,” Nicolaus says with sotto voce awe, “the distance from the highest mountains to the deepest oceans would be 4 meters.”

And yet it was not precise enough to kill off Le Grand K. The trouble was not with Leistner’s surface polish but with the atoms themselves. Silicon comes in three isotopes, each with a different number of neutrons and therefore a different atomic weight. The most common isotope, comprising approximately 92.23 percent of the silicon found in nature, is Si28, with Si29 and Si30 making up the remainder. The problem, naturally, is with the word approximately. The best approximation of the number of atoms in a kilo of mixed-isotope silicon is still an order of magnitude too vague.

Then one morning in 2003, Becker — a consummate networker who by then was head of the international Avogadro project — got a call from a colleague who’d worked in the former East Germany. “Have you considered pure Si28?” asked the man, who said he had connections with a Russian nuclear weapons facility that happened to have a centrifuge for enriching uranium. The cold war was over. The centrifuge was idle. For the right price, the machinery could be modified to enrich silicon. Becker got on the phone with friends at national labs in Italy, Australia, and Japan, eight institutions in all. He raised the equivalent of $2.4 million, in return for which the scientists eventually received 5 kilograms of 99.9995 percent pure silicon 28. Leistner got out his cones and crafted two new spheres. Nicolaus fired up his laser interferometer, the device used to determine their volume. Other labs measured the spheres’ crystal lattice, density, and mass, double-checking one another’s figures. Last January they released their results. They’d gone from being 10 times shy of the all-important eighth significant digit to falling short by a mere factor of three. Team Avogadro hopes the next effort crosses the threshold.

But Nicolaus is now facing a future without Leistner, who is in his 70s and has retired without having been able to train an apprentice with comparable skills. “Machines are reaching a new level of precision,” he says hopefully. “With ion etching” — essentially sandblasting with argon gas ions — “you can put something in a vacuum and remove material atom by atom.” Today ion etching is used to manufacture aspherical lenses. To carve out a silicon sphere will take some fine-tuning — a mere technicality. “We can reduce our uncertainty by a factor of three within the next three years,” Nicolaus says. “No problem.”

Team Planck is based in Gaithersburg, Maryland, where a physicist with the National Institute of Standards and Technology named Richard Steiner has an altogether different idea about how to supplant Le Grand K. His laboratory — a white vinyl-sided house with windows covered in aluminum foil — could be mistaken for a meth lab. But it quickly becomes apparent that it operates on a far more precise level. Visitors are asked to park a good hundred yards away, one of countless precautions intended to protect the building from external disturbances such as vibrations and magnetism. This building is Steiner’s private realm, where he has spent the past 18 years refining a two-story-tall apparatus called a watt balance, which compares electrical and mechanical power. “A lot of the watt balance is actually 100-year-old technology,” Steiner says as he leads the way through a dark and cluttered lab. “We’re mostly applying simple ideas that would have been understood by classical physicists. The difference is that they cared only whether the effect worked, whereas we need to measure it with 10-8uncertainty.”

On the upper floor is a room-sized scale dominated by a wheel fabricated of milled aluminum. Below the wheel is a hand-sized pan supporting a platinum-iridium mass positioned like an apple on a produce scale. One floor below, superconducting electromagnets counteract the downward tug of the platinum-iridium. In other words, the gravitational force on the mass is balanced with the electrical force produced by current in the copper coil. Once calibrated against the international prototype, the electronic kilogram can be defined in terms of the voltage required to levitate Le Grand K — a numerical value, governed by a natural constant, that can be used to calibrate any future watt balance — and the international prototype can at last be sent into retirement.

Of course, the voltage must be measured very precisely, and that takes quantum physics. “I got hired here to work on that,” Steiner says. Back in 1984, long before there was any thought of dethroning Le Grand K, he was given the task of improving electrical measurements using a quantum phenomenon discovered by British physicist Brian Josephson in the ’60s. According to the Josephson effect, voltage can be produced in something called a superconducting junction by bombarding it with microwave radiation. The higher the frequency of that radiation — a number that can be measured with great precision — the higher the voltage. Mathematically, this relationship between frequency and energy is expressed using Planck’s constant.

In fact, back in the ’80s, the watt balance was used as a machine to better determine Planck’s constant by weighing the platinum-iridium kilo. A brilliant experiment, the measurement came with a dividend: The whole thing could theoretically be reversed, effectively using the new-and-improved Planck constant to define the kilogram electronically.

Twenty-seven years into his career at NIST, Steiner is still trying to accomplish that. Shortly after publishing an impressive first round of data in 1998, he celebrated as only a true metrologist would — by taking the apparatus apart and rebuilding it from scratch. In the process, he made some key improvements, such as enclosing the balance in a fiberglass vacuum chamber. Other changes, such as isolating the watt balance from the rest of the building by pouring a separate concrete foundation, had less payoff. “It turns out that if you want to isolate the room from vibrations, you have to dig 10 meters down,” Steiner says, and then he shows me several graphs charting his never-ending struggle against vibration. He points out the rumbling of earthquakes half a world away and the burbling of liquid helium boiling off in the adjoining room. “For every improvement you make you get better signal-to-noise, but then you see something else,” he says.

Little by little, Steiner has refined his watt balance to reduce uncertainty to a level that is almost as good as what’s achieved with silicon spheres at Bundesanstalt, tantalizingly near the target.

Regardless of the numbers, Steiner argues, the watt balance, with its Planck constant, is “a better realization,” because his system is self-contained and replicable, whereas the Avogadro project spans several continents and relies on a single artifact. In any case, the need for a more precise definition of the kilogram is becoming increasingly critical as more transistors switching at higher speeds are packed onto a single chip, leaving an ever-decreasing margin of error. With an erratic kilogram, calibrating inputs and outputs becomes even trickier. Le Grand K’s unreliability “will start to be noticeable in the next decade or two in the electronics industry,” he says.

The solution to that eventual problem, says Peter Becker of the Avogadro camp, is — no surprise — to redefine the kilogram based on the Avogadro constant. A definition based on a silicon sphere is simpler and fundamentally better than the watt balance approach. “Four basic experiments are a lot easier to handle than one complicated experiment,” he asserts. “We can check things independently.” He also emphasizes the explicit relationship between the spheres and the kilo. “You have only to count the atoms. No other knowledge is necessary.”

Both sides admit that a knockdown fight is premature. “At the moment, we should work together,” Nicolaus says. Initially, the new definition will actually depend on the agreement of the two experiments: In principle, each can be used to check the other. Agreement would reassure metrologists that the new kilogram was scientifically sound before either of the two methods was selected as the technique by which the world’s weights are calibrated.

The elder statesmen of metrology are justifiably anxious to reach the end. They have worked so long to replace Le Grand K. “The time to act in principle is now,” Becker says. Adds Quinn: “We’re so close!” Steiner and Nicolaus are less frantic. In particular, neither is as certain as their elders that their numbers will eventually converge — that mechanical force and electrical force are absolutely equivalent, as assumed. “If we were to see that all the watt balance measurements were leveling at one level and all the Avogadro measurements at another level, then there must be a new physical law,” Nicolaus says. Steiner concurs. “If there is truly a difference between counting atoms and making watt balance measurements,” he says, “then there is some fundamental difference between making an energy measurement and making a mass measurement. It would be real basic science.”

It would also be an apt coda to the revolution in measurement fomented by the French Revolution. As it happens, the savants bungled their measurement of the planet, resulting in a platinum meter that was 0.2 millimeters shorter than the fractional distance from the North Pole to the equator. In part, this error in the meter was due to the mistaken assumption, widespread at the time, that Earth was a regular spheroid—an error that the savants’ efforts ultimately helped to correct. “Pushing measurement very far gets you to weird things,” observes Alder, the Northwestern historian. Weirder even, and certainly more wonderful, than the cosmic joke of a kilogram losing weight at the expense of the universe.

Jonathon Keats (jonathon_keats@yahoo.com) writes Wired’s Jargon Watch column and is the author of Virtual Worlds: Language at the Edge of Science and Technology.